| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | One unknown from sum constraint only |
| Difficulty | Easy -1.3 This is a straightforward recall question requiring only that probabilities sum to 1 (giving a simple linear equation 0.1 + 0.3 + 2p + p = 1) and then computing E(X) using the standard formula. Both parts are direct application of basic definitions with no problem-solving or conceptual challenge. |
| Spec | 5.02b Expectation and variance: discrete random variables |
| \(x\) | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( X = x )\) | 0.1 | 0.3 | \(2 p\) | \(p\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0.1 + 0.3 + 2p + p = 1\) oe | M1 | |
| \(p = 0.2\) | A1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\Sigma xp\) | M1 | \(\geq 2\) terms correct, FT \(p\) |
| \(= 2.7\) oe | A1f [2] |
## Question 1:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.1 + 0.3 + 2p + p = 1$ oe | M1 | |
| $p = 0.2$ | A1 [2] | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\Sigma xp$ | M1 | $\geq 2$ terms correct, FT $p$ | eg $\div 4$: M0A0 |
| $= 2.7$ oe | A1f [2] | |
---1 The probability distribution of a random variable $X$ is shown in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$x$ & 1 & 2 & 3 & 4 \\
\hline
$\mathrm { P } ( X = x )$ & 0.1 & 0.3 & $2 p$ & $p$ \\
\hline
\end{tabular}
\end{center}
(i) Find $p$.\\
(ii) Find $\mathrm { E } ( X )$.
\hfill \mbox{\textit{OCR S1 2012 Q1 [4]}}